A method for calculating the spacing between spliced ​​CCD chips based on a geometric distortion model

Abstract

The present application discloses a method for solving the spacing of spliced ​​CCD chips based on a geometric distortion model, and relates to the field of astronomical measurement technology. The star images in the CCD image are matched with the stars in the astronomical measurement catalog through a triangle matching algorithm; the geometric distortion model of each chip unit is calculated; and the measurement coordinate system of each chip is jointly spliced ​​by using the principle that the geometric distortion of the optical system is symmetrical with the optical center as the center. The present application utilizes the principle that the spliced ​​CCD chip units share the telescope imaging system, and is implemented on the basis of the distortion model export by analyzing the continuity of the chip unit distortion model. The method provided in the present application can derive the relationship between the chips without the need for observation data and finally derive a global measurement coordinate system that conforms to all chip units, effectively reducing the processing flow and the amount of data calculation.

Description

Technical Field

[0001] The present application relates to the field of astronomical measurement technology, and more specifically, to a method for solving the spacing between spliced ​​CCD chips based on a geometric distortion model. Background Art

[0002] With the development of technology and the need for scientific research, the construction aperture of telescopes has also increased accordingly. Usually, large-aperture telescopes are equipped with large-surface charge-coupled devices (CCDs) composed of multiple smaller pixel-size CCDs. The astronomical measurement method of spliced ​​CCDs is generally performed separately in each CCD unit, but accurately solving the positional relationship between CCD units (i.e., chip spacing), and then combining all CCD units for global astronomical measurement, will significantly increase the calibration reference stars and can greatly improve the astronomical measurement accuracy of the telescope.

[0003] There are very few studies on measuring the spacing between stitched CCD chips, and there are three main methods. One of the more complete methods was proposed by Anderson and King of the Hubble Space Telescope Science Team in the study of geometric distortion solution. This method does not use a reference star catalog, but directly observes a dense star cluster through dithering, and then constructs a position reference set with approximately distortion-free errors through the pixel positions of the stars on the image. This position set is called the master frame. The GD solution is performed by iteratively comparing the observed image and the master frame position. Furthermore, the GD effect of different CCD units is corrected, so that each CCD unit is converted to a common master frame system. This method is one of the pipeline programs for detecting the HST optical system, and is also used in many important scientific projects, such as the famous Hubble Ultra Deep Field image construction.

[0004] Another method was proposed by Platais in his work on establishing the standard deviation of astronomical measurements for the Mayer telescope in the United States. This method introduces an initial chip spacing parameter for each chip , that is, the horizontal deviation, vertical deviation and rotation angle deviation of each chip, so as to convert the pixel position of the star observed by each chip into the common pixel coordinate system formed by all chips, and finally connect it with the ideal coordinate system calculated by the star catalog, and through iterative solution, minimize the error of the film constant solution of this common pixel coordinate system.

[0005] The last method was proposed by Zheng Zhongjie in his study of the geometric distortion of the Bok 2.3-meter telescope on Kitt Peak in the United States. This method uses the adjacent pixel edges of the chip and the geometric distortion model of each chip, and connects the two adjacent edges through the standard plane in the classical astronomical measurement process, thereby estimating the positional relationship between the two adjacent edges, and finally deriving the chip spacing, that is, the rotation angle and the average spacing. The disadvantage of this method is that the calculation process is relatively complicated and the result cannot be further obtained to obtain a global measurement coordinate system that conforms to all chip units. Summary of the invention

[0006] In view of this, the present application provides a method for solving the spacing of spliced ​​CCD chips based on a geometric distortion model, which is implemented on the basis of the distortion model export. The relationship between the chips can be obtained without observation data and a global measurement coordinate system that conforms to all chip units can be finally derived, effectively reducing the processing flow and data calculation amount.

[0007] To achieve the above objectives, the proposed solution is as follows:

[0008] A method for solving the spacing of spliced ​​CCD chips based on a geometric distortion model, comprising:

[0009] Acquire CCD images of target star clusters;

[0010] The pixel positions of the stars in the CCD image are determined by the Gaussian centering algorithm;

[0011] Obtain the astrometric star catalog corresponding to the observed sky area;

[0012] The star images in the CCD image are matched with the stars in the astrometric star catalog by using a triangle matching algorithm;

[0013] Calculate the geometric distortion model of each chip unit;

[0014] By utilizing the principle that the geometric distortion of the optical system is symmetrical with the optical center as the center, the measurement coordinate systems of each chip are jointly spliced.

[0015] Preferably, matching the star images in the CCD image with the stars in the astrometric star catalog by a triangle matching algorithm includes:

[0016] Determine the corresponding positions of the three stars in the CCD image in the astrometric star catalog and obtain the astrometric information of the three stars;

[0017] The station-centered apparent positions of these three stars are calculated based on the astrometric information;

[0018] The target coordinates of the star projected onto the standard tangent plane are calculated using the projection formula. The projection formula is:

[0019] ,

[0020] Among them, A and D are the right ascension and declination directions of the telescope optical axis, respectively. To stand in the heart and see the position;

[0021] The relationship between the measurement coordinates of the CCD image and the target coordinates is established through the six-constant film model.

[0022] Preferably, calculating the geometric distortion model of each chip unit includes:

[0023] Calculate the first pixel coordinate of the star image according to the target coordinates through a four-constant model;

[0024] A reference star residual is obtained according to a residual value calculated from the first pixel coordinate and the second pixel coordinate, wherein the second pixel coordinate is the pixel coordinate of the star image actually observed according to the CCD image;

[0025] Decompose the reference star residuals;

[0026] Calculate the geometric distortion of each reference star in the field of view at the pixel position in each CCD image;

[0027] Each CCD chip is divided into grid points, and each reference star determines the target grid point of each reference star according to the pixel position;

[0028] Calculate the average value of the geometric distortion of the reference star in each grid point;

[0029] The pixel position of each reference star is bilinearly interpolated according to the geometric distortion average value of adjacent grid points, and the pixel position of each reference star is corrected until the distortion average value of each grid point is less than a preset threshold, thereby obtaining a distortion model of each chip unit;

[0030] The distortion model of each chip unit is respectively fitted with a polynomial to obtain a geometric distortion model of each chip.

[0031] Preferably, the reference star residual includes: geometric distortion error, star catalog error, and measurement error.

[0032] Preferably, calculating the geometric distortion of each reference star in the field of view at a pixel position in each CCD image includes:

[0033] Calculate the reference star residual of the pixel position of the current reference star in the i-th and j-th images and :

[0034] ,

[0035] ,

[0036] in, , are the geometric distortion errors of the current reference star in the i-th and j-th images, respectively. , are the measurement error terms of the i-th and j-th images respectively, and Represent the parameter estimates of the i-th and j-th images respectively, and They represent the declination coordinates of the tangent points of the celestial tangent plane corresponding to the i-th and j-th images, respectively. ;

[0037] Combining the two equations, we get the common catalog error term:

[0038] ;

[0039] Determine the relationship between the geometric distortion error terms of the current reference star in the i-th and j-th images:

[0040] ,

[0041] in, , Respectively represent the position residuals of the current reference star in the i-th and j-th images;

[0042] The geometric distortion error term of the current reference star in the N-1 ith image is The geometric distortion error term with the current reference star in the other N-1 j images The relationship between them is summed up:

[0043] ;

[0044] Estimate the geometric distortion of the current reference star in the i-th image:

[0045] ,

[0046] The above process is executed repeatedly until the geometric distortion of the current reference star in the other N-1 images and the geometric distortion of all reference stars in the field of view in all images are determined.

[0047] Preferably, the distortion model of each chip unit is respectively fitted with a polynomial to obtain a geometric distortion model of each chip:

[0048] .

[0049] Preferably, the measurement coordinate systems of the chips are jointly spliced ​​by utilizing the principle that the geometric distortion of the optical system is symmetrical with the optical center as the center, including:

[0050] The geometric distortion model of chip i is symmetrically transformed with the optical center as the center to obtain the symmetrical transformation model:

[0051] ,

[0052] in, is the geometric distortion model of chip i, is the physical distance from the optical center to chip i, is the length of chip i, is the length of chip i, is the optical center position of chip i in the measurement coordinate system, = ;

[0053] Geometric distortion model and chip based on chip i symmetry transformation j The geometric distortion model establishes six constant relationships:

[0054] ,

[0055] Among them, the chip i and Chip j Symmetrical with the optical center as the center, the chip i and Chip j The geometric distortion model is symmetrical with the optical center as the center. are six constant relationship parameters, Chip-based i Symmetric transformation model Derived Chip j The distortion model of

[0056] Set the distortion effect and the first-order derivative of the optical center position in the optical system to 0 and build the chip i and Chip j Relationship:

[0057] ;

[0058] Chip i and Chip j Substitute the optical center position in the corresponding measurement coordinate system into:

[0059] ,

[0060] Among them, the optical center position of chip i in the measurement coordinate system is ,chip j The optical center position under the measurement coordinate system is ;

[0061] According to the relative position of the optical center relative to the chip i, the relative position of the optical center relative to the chip j The relative position and chipi Relative chip j The rotation angle of the chip is converted j Measurement coordinates relative to chip i:

[0062] ,

[0063] in, is the relative position of the optical center relative to chip i, Optical center relative to chip j The relative position of For Chip j The measurement coordinates relative to chip i;

[0064] Joint chip i and Chip j The measurement coordinate system is constructed based on the chip i Joint chip for reference ij .

[0065] It can be seen from the above technical solutions that the method for solving the spacing between spliced ​​CCD chips based on the geometric distortion model provided by the present application matches the star images in the CCD image with the stars in the astronomical star catalog through a triangle matching algorithm; calculates the geometric distortion model of each chip unit; and uses the principle that the geometric distortion of the optical system is symmetrical around the optical center to jointly splice the measurement coordinate systems of each chip. The present application utilizes the principle that spliced ​​CCD chip units share a telescope imaging system, and is implemented on the basis of distortion model derivation by analyzing the continuity of the chip unit distortion model. The method provided by the present application can derive the relationship between the chips without observation data and ultimately derive a global measurement coordinate system that conforms to all chip units, effectively reducing the processing flow and the amount of data calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0067] Figure 1 A flow chart of a method for solving the spacing of spliced ​​CCD chips based on a geometric distortion model provided in an embodiment of the present application;

[0068] Figure 2 A CCD image of a target star cluster provided in an embodiment of the present application;

[0069] Figure 3A schematic diagram of a projection process of celestial coordinates to a standard tangent plane provided in an embodiment of the present application;

[0070] Figure 4 A schematic diagram of a distortion model derived from a spliced ​​CCD provided in an embodiment of the present application;

[0071] Figure 5 A schematic diagram of another projection process of celestial coordinates to a standard tangent plane provided in an embodiment of the present application;

[0072] Figure 6 A schematic diagram of CCD chip placement provided in an embodiment of the present application. DETAILED DESCRIPTION

[0073] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0074] First, combine Figure 1 A method for solving the spacing of spliced ​​CCD chips based on a geometric distortion model provided in an embodiment of the present application is introduced. Figure 1 As shown:

[0075] Step S01, acquiring a CCD image of a target star cluster.

[0076] Specifically, a dense star cluster can be selected as the target star cluster, and the target star cluster can be observed by shaking, and image acquisition can be performed to obtain a CCD image. Figure 2 The CCD image shown, where the numbers are the pointing order, and the larger the gray value, the more observation times.

[0077] Step S02, determining the pixel positions of the stars in the CCD image by using a Gaussian centering algorithm.

[0078] Step S03, obtaining an astrometric star catalog corresponding to the observed sky area.

[0079] Specifically, the astrometric star catalog Gaia DR3 corresponding to the observed sky area can be obtained from the website https: / / gea.esac.esa.int / archive / , which includes the astrometric information of J2000.0 position, proper motion, parallax, radial velocity and magnitude.

[0080] Step S04, matching the star images in the CCD image with the stars in the astronomical star catalog by using a triangle matching algorithm.

[0081] Specifically, a star image matching algorithm is implemented on the CCD image, and the distribution of stars in the CCD image is matched to the stars in the astrometric star catalog. The star images in the CCD image can be matched with the stars in the astrometric star catalog by a triangle matching algorithm.

[0082] The corresponding positions of the three stars in the CCD image in the astrometric star catalog can be determined by the naked eye, and the astrometric information of the three stars can be obtained. The astrometric information includes right ascension, declination, proper motion, parallax, radial velocity, etc. The station center apparent positions of the three stars are calculated based on the astrometric information.

[0083] The target coordinates of the star projected onto the standard tangent plane can be calculated using the projection formula. The projection process from celestial coordinates to the standard tangent plane is as follows: Figure 3 As shown, the projection formula is:

[0084] ,

[0085] Among them, A and D are the right ascension and declination directions of the telescope optical axis, respectively. To stand at the center of the view position, is the target coordinate of the standard cutting plane.

[0086] The relationship between the measurement coordinates of the CCD image and the target coordinates is established through the six-constant film model. The six-constant film model is:

[0087] ,

[0088] in, are the undetermined parameters of the six-constant film model, is the measurement coordinate.

[0089] The unknown parameters of the six-constant film model can be obtained through the least squares method, and the positions of other reference stars in the image can be roughly estimated. A smaller threshold (such as 1 pixel) can be selected to further complete the matching of other reference stars in the image.

[0090] Step S05, calculating the geometric distortion model of each chip unit.

[0091] Step S06, using the principle that the geometric distortion of the optical system is symmetrical with the optical center as the center, the measurement coordinate systems of the chips are jointly spliced.

[0092] Specifically, a joint chip system can be constructed from several pairs of central chips closest to the center, and then all chips can be gradually added to complete high-precision astronomical measurement by jointly stitching all chip units of the CCD.

[0093] The embodiment of the present application provides a method for solving the spacing between spliced ​​CCD chips based on a geometric distortion model, which matches the star images in the CCD image with the stars in the astrometric star catalog through a triangle matching algorithm; calculates the geometric distortion model of each chip unit; and uses the principle that the geometric distortion of the optical system is symmetrical around the optical center to jointly splice the measurement coordinate systems of each chip. The present application utilizes the principle that spliced ​​CCD chip units share a telescope imaging system, and is implemented on the basis of distortion model derivation by analyzing the continuity of the chip unit distortion model. The method provided in the present application can derive the relationship between the chips without the need for observational data and ultimately derive a global measurement coordinate system that conforms to all chip units, effectively reducing the processing flow and the amount of data calculation.

[0094] The present application embodiment introduces the process of calculating the geometric distortion model of each chip unit in step S05, and the process is as follows:

[0095] Step S051, calculating the first pixel coordinates of the star image according to the target coordinates through a four-constant model.

[0096] Specifically, for a CCD image, the station center-view position from the astrometric star catalog to the observation time is calculated, and then converted to the target coordinates through the center-view section projection A four-constant model is established for the measured coordinates of the CCD image stars and the corresponding target coordinates:

[0097] (1)

[0098] The parameter estimates of the four-constant model can be obtained by the least squares method: and .

[0099] After solving the parameter estimation value of the four-constant model, the first pixel coordinate of the star image can be calculated according to the target coordinates through the four-constant model:

[0100] (2).

[0101] Step S052, obtaining a reference star residual according to the residual value calculated from the first pixel coordinate and the second pixel coordinate.

[0102] Specifically, the second pixel coordinate is the pixel coordinate of the star image actually observed according to the CCD image, that is, the pixel position of the star image in the CCD image is determined by the Gaussian centering algorithm; the difference between the first pixel coordinate and the second pixel coordinate is calculated to obtain the reference star residual:

[0103] (3)

[0104] in, is the second pixel coordinate actually observed according to the CCD image, is the calculated first pixel coordinate.

[0105] Step S053, decomposing the reference star residual.

[0106] Specifically, the reference star residual is usually composed of three error terms: geometric distortion error, catalog error, and measurement error.

[0107] A. Geometric distortion error: The geometric distortion error only depends on the pixel position of the relevant star image on the CCD image and has nothing to do with the astronomical star catalog.

[0108] B. Star catalog error: Star catalog error is related to the astronomical star catalog and has nothing to do with the pixel position on the CCD image of the star image. The star catalog error is calculated in formula (1) as the first pixel coordinate The target coordinates of the tangent plane to the celestial sphere are generated when The star catalog error can be expressed by the following formula (4):

[0109] (4)

[0110] in, is the position residual of the target coordinates of the reference star in the celestial tangent plane, as shown in the following formula (5):

[0111] (5).

[0112] Since the CCD field of view is small, only the first-order effect of the star catalog error on the pixel position is considered. Therefore, the star catalog error expressed by equation (4) can be simplified to equation (6):

[0113] (6).

[0114] C. Measurement error: The measurement error is related to the signal-to-noise ratio of the measured star, that is, it is related to the image quality. The higher the signal-to-noise ratio, the smaller the error.

[0115] Combining the three errors, the position residual of the star image can be expressed by formula (7): :

[0116] (7).

[0117] Step S054, calculating the geometric distortion of each reference star in the field of view at the pixel position in each CCD image.

[0118] Specifically, it is necessary to count multiple CCD images with overlapping areas to derive the geometric distortion term The data usually used to calculate geometric distortion are taken with the cross observation method, so the same star will be imaged at different positions on the CCD. For the star images that appear in different CCD images, let i and j represent two different images.

[0119] Calculate the reference star residual of the pixel position of the current reference star in the i-th and j-th images and :

[0120] (8)

[0121] (9)

[0122] in, , are the geometric distortion errors of the current reference star in the i-th and j-th images, respectively. , are the measurement error terms of the i-th and j-th images respectively, and Represent the parameter estimates of the i-th and j-th images respectively, and They represent the declination coordinates of the tangent points of the celestial tangent plane corresponding to the i-th and j-th images, respectively. ;

[0123] The geometric distortion error term and the measurement error term in equations (8) and (9) are related to the image where the reference star is located. Since the observation time interval between different CCD images is short, the star catalog error changes little, so the second star catalog error is usually considered to be the same. Equations (8) and (9) can be combined to propose a common star catalog error term:

[0124] (10).

[0125] Since the measurement error is random, the cumulative value of the measurement error term of the same reference star in multiple CCD images is approximately 0 and can be ignored. The geometric distortion error term of the current reference star in the i-th and j-th images can be determined as and The relationship between:

[0126] (11)

[0127] in, , Respectively represent the position residuals of the current reference star in the i-th and j-th images.

[0128] Since the same reference star will appear in N different CCD images, let i be a certain CCD image, we can get N-1 geometric distortion error terms for the current reference star in the i-th image: The geometric distortion error term between the current reference star and the remaining N-1 images The relationship between and . The geometric distortion error term of the current reference star in the N-1 ith image is The geometric distortion error term with the current reference star in the other N-1 j images The relationship between them is summed up:

[0129] (12).

[0130] Since the positions of the same reference star in different images are approximately uniformly distributed, its geometric distortion error is also approximately uniformly distributed in positive and negative values. Then the geometric distortion error term of the reference star in the other N-1 images is It can be considered random, so when N is large, its sum approaches 0, that is, its term can be ignored, so the geometric distortion of the current reference star in the i-th image can be estimated:

[0131] (13)

[0132] in, and Respectively represent the residual value of the reference star in the i-th and j-th images, and Represent the parameter estimates of the i-th and j-th images respectively, and They represent the declination coordinates of the tangent points of the celestial tangent plane corresponding to the i-th and j-th images respectively.

[0133] The above steps S051 to S054 are executed cyclically until the geometric distortion of the current reference star in the other N-1 images and the geometric distortion of all reference stars in the field of view in all images are determined.

[0134] Step S055, dividing each CCD chip into grid points, and determining the target grid points of each reference star according to the pixel position.

[0135] Specifically, each CCD chip can be divided into grid points, and each reference star can be determined according to the pixel position to determine the target grid point corresponding to each reference star. The grid points are assigned to the corresponding target grid points according to the pixel positions of the reference stars.

[0136] Step S056, calculating the average value of the geometric distortion of the reference star in each grid point.

[0137] Specifically, the geometric distortion error term of the reference star is counted at each grid point to obtain the average value of the grid point: .

[0138] Step S057, bilinear interpolation is performed on the pixel position of each reference star according to the geometric distortion average value of adjacent grid points, and the pixel position of each reference star is corrected until the distortion average value of each grid point is less than a preset threshold, thereby obtaining a distortion model of each chip unit.

[0139] Specifically, the pixel position of each reference star can be bilinearly interpolated according to the geometric distortion average value of the adjacent four grid points, the pixel position of the reference star can be corrected, and the next iteration can be entered until the distortion average value of each grid point is less than a preset threshold (such as 0.01 pixel), and the distortion model of each chip unit can be obtained. Figure 4 Shown: Distortion model derived from the stitched CCD of the Bok 2.3-meter telescope.

[0140] Step S058, polynomial fitting is performed on the distortion model of each chip unit, and the obtained geometric distortion model of each chip is:

[0141] (14).

[0142] The embodiment of the present application introduces the process of jointly splicing the measurement coordinate systems of each chip in step S06 by using the principle that the geometric distortion of the optical system is symmetrical with the optical center as the center. The process is as follows:

[0143] like Figure 6 As shown, the chip i and Chip j Symmetrically arrange the chip i and perform a symmetrical transformation on the geometric distortion model of the chip i with the optical center as the center to obtain a symmetrical transformation model:

[0144] (15)

[0145] in, is the geometric distortion model of chip i, is the physical distance from the optical center to chip i, is the length of chip i, is the length of chip i, is the optical center position of chip i in the measurement coordinate system, = .

[0146] Geometric distortion model and chip based on chip i symmetry transformation jThe geometric distortion model establishes six constant relationships:

[0147] (16)

[0148] Among them, the chip i and Chip j Symmetrical with the optical center as the center, the chip i and Chip j The geometric distortion model is symmetrical with the optical center as the center. are six constant relationship parameters, Chip-based i Symmetric transformation model Derived Chip j The distortion model.

[0149] Set the distortion effect and the first-order derivative of the optical center position in the optical system to 0 and build the chip i and Chip j Relationship:

[0150] (17).

[0151] Chip i and Chip j Substitute the optical center position in the corresponding measurement coordinate system into:

[0152] (18)

[0153] Among them, the optical center position of chip i in the measurement coordinate system is ,chip j The optical center position under the measurement coordinate system is ;

[0154] According to the relative position of the optical center relative to the chip i, the relative position of the optical center relative to the chip j The relative position and chip i Relative chip j The rotation angle of the chip is converted j Measurement coordinates relative to chip i:

[0155] (19)

[0156] in, is the relative position of the optical center relative to chip i, Optical center relative to chip j The relative position of For Chip j Coordinates of measurements relative to chip i.

[0157] Joint chip i and Chipj The measurement coordinate system is constructed based on the chip i Reference joint chip system .

[0158] The present application embodiment introduces the implementation process of the method for solving the spacing of spliced ​​CCD chips based on the geometric distortion model, and the process is as follows:

[0159] CCD chip unit i and chip unit j Imaging within the same telescope optical system. Chip unit i and chip unit j The projection process from the same celestial coordinates to the standard tangent plane is as follows Figure 5 As shown. Among them, the chip unit i and chip unit j The geometric distortion error is symmetrical around the optical center.

[0160] like Figure 6 As shown, the chip i and Chip j Symmetrically placed, so the chip i and Chip j The distortion model should also be based on the optical center O is centrally symmetrical. Let the optical center O Distance chip i The physical distance is , i.e., the optical center O The distance from the lower right corner of chip i is . Because the chip unit i The measurement coordinates have their origin in the lower left corner and are , Gao Wei , then relative to the chip i The measurement coordinates, optical center O The location is Similarly, relative to the chip j The measurement coordinates of the optical center are Because the chip i and Chip j The distortion model is based on the optical center O is centrally symmetrical, so the chip can be i Distortion model With the heart of light O Perform a symmetric transformation around the center:

[0161] (15).

[0162] Formula (14) is gridded. For example, the chip i of and Divided into 100 grid points, the chip i Divide into grid points. i The distortion model is based on the optical center O The distorted model after symmetric transformation at the center Similarly, the chip j of and Divided into 100 grid points, the chip j Divide into Grid points. You can also get the chip j Distortion Model It can be seen that After the centrosymmetric transformation, ,Right now = Because the chip i and Chip j The distortion model is considered to be symmetric about the optical center. and By establishing a simple six-constant relationship and considering the effects of translation, rotation, scaling and shearing, we can obtain equation (16):

[0163] (16).

[0164] because and As known conditions, the six constant relations can be obtained . Further, according to the six constant relationship parameters After transformation, we can get chip-based i Centrosymmetric transformation model Derived Chip j Distortion model This model and chip i The geometric distortion model of the optical center O Center symmetry, relative to the chip j The measurement coordinate system of .

[0165] Since the optical center position of the optical system is usually considered to have no distortion error, and the first-order derivative of the distortion of the optical center position is 0. i and Chip j Establish the following relationship

[0166] (17).

[0167] Since relative to the chip i The measurement coordinate system of the optical center is ,chip jThe distorted model obtained after transformation Relative to chip j The measurement coordinate system of the optical center is Substituting the two optical center positions into equation (17), we can obtain:

[0168] (18).

[0169] Solving equation (18), we can calculate , that is, the optical center relative to the chip i According to the previous steps, we can also calculate , that is, the optical center relative to the chip j location.

[0170] According to the optical center relative to the chip i Location , Optical center relative to chip j Location and Chip i Relative chip j The rotation angle , converted to chip j Relative to chip i The measurement coordinates of .

[0171] (19).

[0172] The final joint chip i and Chip j The measurement coordinate system is constructed based on the chip i Reference joint chip system First, the combined chip system is constructed from the pairs of chips closest to the center, and then all the chips are gradually added to complete the high-precision astronomical measurement of all chip units of the combined splicing CCD.

[0173] Finally, it should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0174] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0175] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for solving the spacing of spliced ​​CCD chips based on a geometric distortion model, characterized in that: include: Acquire CCD images of target star clusters; The pixel positions of the stars in the CCD image are determined by the Gaussian centering algorithm; Obtain the astrometric star catalog corresponding to the observed sky area; The star images in the CCD image are matched with the stars in the astrometric star catalog by using a triangle matching algorithm; Calculate the geometric distortion model of each chip unit; Using the principle that the geometric distortion of the optical system is symmetrical with the optical center as the center, the measurement coordinate systems of each chip are jointly spliced; The process of calculating the geometric distortion model of each chip unit includes: Calculate the first pixel coordinate of the star image according to the target coordinate through a four-constant model; A reference star residual is obtained according to a residual value calculated from the first pixel coordinate and the second pixel coordinate, wherein the second pixel coordinate is the pixel coordinate of the star image actually observed according to the CCD image; Decompose the reference star residuals; Calculate the geometric distortion of each reference star in the field of view at the pixel position in each CCD image; Each CCD chip is divided into grid points, and each reference star determines the target grid point of each reference star according to the pixel position; Calculate the average value of the geometric distortion of the reference star in each grid point; The pixel position of each reference star is bilinearly interpolated according to the geometric distortion average value of adjacent grid points, and the pixel position of each reference star is corrected until the distortion average value of each grid point is less than a preset threshold, thereby obtaining a distortion model of each chip unit; The distortion model of each chip unit is respectively fitted with a polynomial to obtain a geometric distortion model of each chip.

2. The method for solving the spacing between spliced ​​CCD chips based on a geometric distortion model according to claim 1, characterized in that: The star images in the CCD image are matched with the stars in the astrometric star catalog by using a triangle matching algorithm, including: Determine the corresponding positions of the three stars in the CCD image in the astrometric catalog and obtain the astrometric information of the three stars: The station-centered apparent positions of these three stars are calculated based on the astrometric information; The target coordinates of the star projected onto the standard tangent plane are calculated using the projection formula. The projection formula is: Among them, A and D are the right ascension and declination directions of the telescope optical axis, and (α, δ) is the station center apparent position; The relationship between the measurement coordinates of the CCD image and the target coordinates is established through the six-constant film model.

3. The method for solving the spacing between spliced ​​CCD chips based on a geometric distortion model according to claim 2, characterized in that: The reference star residual includes: geometric distortion error, star catalog error, and measurement error.

4. The method for solving the spacing between spliced ​​CCD chips based on a geometric distortion model according to claim 3 is characterized in that: Calculate the geometric distortion of each reference star in the field of view at the pixel position in each CCD image, including: Calculate the reference star residual (Δx) of the pixel position of the current reference star in the i-th and j-th images i :Δy i ) and (Δx j :Δy j ): Among them, (dx i ,dy i )、(dx j :dy j ) are the geometric distortion errors of the current reference star in the i-th and j-th images, respectively, (v xi , v yi )、(v xj :v yj ) are the measurement error terms of the i-th and j-th images, respectively. is the parameter estimate obtained by the least squares method, D i With D j Respectively represent the declination coordinates of the tangent points of the celestial tangent plane corresponding to the i-th and j-th images, j≠i; Combining the two equations, we get the common catalog error term: Determine the relationship between the geometric distortion error terms of the current reference star in the i-th and j-th images: Among them, (Δx i , Δy i )、(Δx j , Δy j ) represent the position residuals of the current reference star in the i-th and j-th images respectively, and Respectively represent the parameter estimates of the i-th and j-th images; The geometric distortion error term (dx i ,dy i ) and the geometric distortion error term (dx) of the current reference star in the other N-1 j images j ,dy j ) are accumulated and summed: Estimate the geometric distortion of the current reference star in the i-th image: The above process is executed repeatedly until the geometric distortion of the current reference star in the other N-1 images and the geometric distortion of all reference stars in the field of view in all images are determined.

5. The method for solving the spacing between spliced ​​CCD chips based on a geometric distortion model according to claim 4 is characterized in that: The distortion model of each chip unit is fitted with a polynomial, and the geometric distortion model of each chip is obtained as follows: Among them, (x, y) is the measured coordinates of the image star.

6. The method for solving the spacing between spliced ​​CCD chips based on a geometric distortion model according to claim 5, characterized in that: Using the principle that the geometric distortion of the optical system is symmetrical with the optical center as the center, the measurement coordinate systems of each chip are jointly spliced, including: The geometric distortion model of chip i is symmetrically transformed with the optical center as the center to obtain the symmetrical transformation model: Among them, (f i , g i ) is the geometric distortion model of chip i, (Δx i , Δy i ) is the physical distance from the optical center to chip i, W i is the length of chip i, H i is the height of chip i, (W i +Δx i , -Δy i ) is the optical center position of chip i in the measurement coordinate system, (dx i ′,dy i ′)=(-dx i , -dy i ); Based on the geometric distortion model of chip i after symmetric transformation and the geometric distortion model of chip j, a six-constant relationship is established: Among them, chip i and chip j are symmetrical with the optical center as the center, and the geometric distortion model of chip i and chip j is symmetrical with the optical center as the center, (a ji , b ji , c ji , d ji :e ji , f ji ) are six constant relationship parameters; The distortion effect of the optical center position in the optical system and the first-order derivative of the distortion are set to 0, and the relationship between chip i and chip j is established: Among them, (dx ji ,dy ji ) is the symmetric transformation model based on chip i (dx i ′,dy i ′) The derived distortion model of chip j; Substitute the optical center positions of chip i and chip j in the measurement coordinate system: Among them, the optical center position of chip i in the measurement coordinate system is (W i +Δx i , -Δy i ), the optical center position of chip j in the measurement coordinate system is (-Δx i , H j +Δy i ), H j is the height of chip j; According to the relative position of the optical center relative to chip i, the relative position of the optical center relative to chip j and the rotation angle of chip i relative to chip j, the measured coordinates of chip j relative to chip i are converted: Among them, (Δx i :Δy i ) is the relative position of the optical center relative to chip i, (Δx j :Δy j ) is the relative position of the optical center relative to chip j, (x ji :y ji ) is the measurement coordinate of chip j relative to chip i; Combine the measurement coordinate systems of chip i and chip j to construct a combined chip system C with chip i as the reference ij .

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